If s and t are positive integers such that s/t = 64.12 which

Question

If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t ?

(A) 2
(B) 4 
(C) 8 
(D) 20 
(E) 45

Bunuel · Accepted Answer

SOLUTION

If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t ?

(A) 2
(B) 4 
(C) 8 
(D) 20 
(E) 45

s  divided by  t  yields the remainder of  r  can always be expressed as:  \frac{s}{t}=q+\frac{r}{t}  (which is the same as  s=qt+r ), where  q  is the quotient and  r  is the remainder.

Given that  \frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25} , so according to the above  \frac{r}{t}=\frac{3}{25} , which means that  r  must be a multiple of 3. Only option E offers answer which is a multiple of 3

Answer. E.

fameatop · Answer

Shortcut for this question:-
64.12 = 64 + 12/100
Now focus on remainder part which is 12/100= 3/25 
Because 3 represents some fraction (ratio) of remainder , the remainder must be a multiple of 3. only 45 is a multiple of 3.

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KarishmaB · Answer

If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t ?

(A) 2
(B) 4 
(C) 8 
(D) 20 
(E) 45

When we say  \frac{s}{t} = 64.12 = 64 \frac{12}{100} = 64 \frac{3}{25} 
We get  \frac{s}{t} = 64 \frac{3}{25} 
What does the mixed fraction of the right hand side signify? It signifies that s > t and when s is divided by t, we get 64 as quotient and 3 as remainder if t is 25.

e.g.  \frac{13}{5} = 2 \frac{3}{5} . Here, remainder is 3
  \frac{130}{50} = 2 \frac{30}{50} . Here remainder is 30.
 \frac{26}{10} = 2 \frac{6}{10} . Here remainder is 6.
So in our question, the remainder will be 3 or any multiple of 3. 45 is the only multiple of 3.

EvaJager · Answer

We can rewrite the given equality as  s = 64t + 0.12t . The divider is t, the quotient is 64.
The remainder is  0.12t  (it is less than t) and it is an integer, being equal to  s-64t .
Since  0.12t=\frac{3}{25} t , it follows that t should be a multiple of 25, so  t=25n , for some positive integer n.
Therefore, the remainder is  3n , or a multiple of 3. The only answer that is a multiple of 3 is 45.

Answer: E

mbaiseasy · Answer

\frac{S}{t} = 64 + .12 
 S = 64t + .12t

The remainder is equal to .12t.

R = .12t
R/.12 = t

We have to look for R where R/.12 is an integer.

A)2/.12 = 200/12 is not an integer
B)4/.12 = 400/12 = 100/3 is not an integer
C) 8/.12 = 800/12 = 400/6 = 200/3 is not an integer
D) also not
E) 45/12 = 4500/12 = 1500/4 = 15*25 is an integer

Answer: E
C)

EgmatQuantExpert · Answer

After expressing s/t = 64.12 as: s = 64t + 0.12t In case a student faces doubts about how to draw inferences about remainder r from the above equation, here is an alternate line of thought: It is clear that the remainder r will come from the term 0.12t So, we can write: r = 0.12t => t = \frac{r}{0.12} = \frac{100r}{12} = \frac{25r}{3} So, t = \frac{25r}{3} But, the question statement gives us a constraint on t: that t is a positive integer. This means, \frac{25r}{3} is a positive integer. This is only possible when r is a multiple of 3. As I said, an alternate route to the same deduction. :-D

Hope this was useful for you! Best Regards Japinder

BrushMyQuant · Answer

We know that  \frac{s}{t}  = 64.12, and we need to find the remainder when s is divided by t

s/t = 64.12,
=> s = t*64.12
=> s = 64t + t*.12
So, when s is divided by t then we will get t*.12 as reminder (as t*.12 will be less than t)
Now t is an integer and .12 is 12*.01 which means it is 3*something
So, only answer choices which are multiple of 3 are contenders.

Only possibility is E!
Hope it helps!

Watch the following video to learn the Basics of Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

mohitvig17 · Answer

Answer is E

S/T = 64.12 or you can write it as 6412/100 or 1603/25

So, If we divide 1603 by 25 we will get remainder of 3.

From the five options, only 45 is divisible by 3 So, The answer should be 45.

pavan2185 · Answer

out of the answer explanation, but can we also say that t must be a multiple of 25 using the same fraction?

Bunuel · Answer

Yes, t must be a multiple of 25: s/t = 1603/25 = 3206/50 = 6412/100 = ... = 64.12 --> the remainders 3, 6, 12, ..., respectively.

nehamodak · Answer

I did not understand why r must be a multiple of 3? From answer choice E 45 is 15 times 3 (a multiple of 3) does that mean t will be 15 times 25?

PareshGmat · Answer

Because  \frac{3}{25} cannot be simplified further (say factorised further)

\frac{3}{25}= \frac{3*15}{25*15}= \frac{45}{25*15}  ... That is possible

luckyme17187 · Answer

Answered this question wrong but when i finished reading karishma's blog  https://www.veritasprep.com/blog/2011/05/quarter-wit-quarter-wisdom-knocking-off-the-remaining-remainders/  . I am confident about these type of questions.

s/t=64.12

when we divide "s" by "t" then 64.12, Here .12 is a Remainder which we are representing in quotient. so to find the possible remainder...

0.12--12/100 -- 3/25 , so 25 or multiple of 25 has to be a "t" & 3 or multiple of 3 has to be remainder.

Answer E.

ankushbagwale · Answer

If the question had been which of the following cannot be the remainder. Then can we use the propertry that Remainder must be divisibe by 25 as well???

EgmatQuantExpert · Answer

Dear Ankush Good to see you here on GC! :-D

Here's the answer to your question: It is not necessary for the remainder to be divisible by 25. Let's look at this in terms of constraints: Constraint 1: The remainder is always a non-negative integer. From the equation \frac{r}{t}=\frac{3}{25} , we get that r= \frac{3t}{25} From constraint 1, we see that \frac{3t}{25} must be a non-negative integer. This means either t = 0 or t is a multiple of 25. But t cannot be equal to 0 because then the expression \frac{s}{t} becomes undefined This means, t is a multiple of 25. Constraint 2: The question states that t is a positive integer. As explained in the post I made just above, this means \frac{25r}{3} is a positive integer, which leads you to the inference that r is a multiple of 3. So, the bottom-line is that the only 2 inferences that we can conclusively draw from the given information is that: i) t is a multiple of 25 and ii) r is a multiple of 3 Hope this helped!

Thanks and Best Regards Japinder

GMATinsight · Answer

Decimal part x Divisor = Remainder

i.e. o.12*t = remainder
i.e. Remainder = (12/100)*t = (3/25)*t

Since the Result has to be multiple of 3 so Option E is the only choice that fits the requirement

Answer: Option E

JeffTargetTestPrep · Answer

This problem will be best solved using the remainder formula. Let’s first state the remainder formula:
 
When positive integer x is divided by positive integer y, if integer Q is the quotient and r is the remainder, then x/y = Q + r/y. 
 
In this problem we are given the following:

s/t = 64.12

We can simplify this to read as the remainder formula:

s/t = 64 + 0.12

s/t = 64 + 12/100

s/t = 64 + 3/25
 
Because Q is always an integer, we see that Q must be 64, and thus the remainder r/y must be 3/25. We can now equate r/y to 3/25 and determine a possible value for r.
 
r/y = 3/25

Note that some equivalent values for r/y could be 6/50 or 9/75 or 12/100, and so forth. Note that in all cases, the value of r is a multiple of 3.

Of the answer choices, the only multiple of 3 is 45, so that is a possible value of r.

Answer: E

Sri07 · Answer

any Similar questions?

Bunuel · Answer

Check this one: https://gmatclub.com/forum/if-s-and-t-a ... fl=similar

If s and t are positive integers such that s/t = 64.12 which

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GMAT Problem Solving (PS) Questions

If s and t are positive integers such that s/t = 64.12 which

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